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Nanodynamic mechanical behavior of graphene nanoplatelet-reinforced tantalum carbide
Available online at www.sciencedirect.com
ScienceDirect Scripta Materialia 69 (2013) 678–681 www.elsevier.com/locate/scriptamat
Nanodynamic mechanical behavior of graphene nanoplatelet-reinforced tantalum carbide Andy Nieto,a Debrupa Lahiria,b and Arvind Agarwala,⇑ a
Plasma Forming Laboratory, Nanomechanics and Nanotribology Laboratory, Mechanical and Materials Engineering, Florida International University, 10555 West Flagler Street, EC 3464, Miami, FL 33174, USA b Department of Materials and Metallurgical Engineering, Indian Institute of Technology, Roorkee, Uttarakhand 247667, India Received 6 June 2013; revised 26 July 2013; accepted 27 July 2013 Available online 1 August 2013
Nanodynamic mechanical analysis (nanoDMA) is performed on spark plasma sintered tantalum carbide composites reinforced with graphene nanoplatelets (GNPs). The addition of GNPs enhances damping (tand) at 25–100 Hz frequencies by up to 300%. It also improves damping behavior through energy-dissipating mechanisms, such as GNP bending, kinking and sliding. A model for correlating improvement in the damping behavior with the fracture toughness is presented. GNP energy-dissipating mechanisms are most effective in improving damping behavior when GNPs are dispersed uniformly. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: TaC; NanoDMA; Graphene nanoplatelet; Damping; Tan delta
Ultrahigh-temperature ceramics (UHTCs) have attracted much attention because of their excellent refractory properties and high strength. These properties make them ideal candidates for aerospace systems, such as hypersonic missiles, planetary entry vehicles and rocket propulsion systems [1–3]. One of the factors impeding the implementation of these materials is their low fracture toughness. Several studies have been conducted on composite UHTCs designed to improve fracture toughness and flexure strength [4–9]. One crucial property of UHTCs that has received little attention is their poor damping behavior. UHTCs such as tantalum carbide (TaC) will be utilized in hypersonic systems that are subjected to a barrage of shock waves. Shock waves are unsteady phenomena which impart impulse forces onto the surface generating them. Damping of such impulsive forces is critical to preventing accumulative damage. Hypersonic vehicles and spacecraft are also subjected to substantial amounts of vibrations and flutter, which can cause cracking. Improving the dissipation of vibrations can suppress crack nucleation and thus reduce the amount of critical cracks and defects. Our approach utilizes the addition of graphene nanoplatelets (GNPs) as reinforcement for TaC to enhance both the fracture toughness and the damping behavior.
⇑ Corresponding
author. Tel.: +1 305 348 1701; fax: +1 305 348 1932; e-mail: agarwala@fiu.edu
The details of TaC–GNP composite synthesis, microstructure and fracture toughness can be found elsewhere [10,11]. The motive behind using GNPs as a dampening phase stems from the excellent damping behavior of multi-layer graphene [12]. Lahiri et al. [12] showed that multi-layer graphene membranes improved the damping behavior of a rigid Si/SiO2 surface by up to 260%. The improvement in damping behavior (tan d) was seen at various dynamic loads (0.1–50 lN) and for a range of frequencies (50–250 Hz). The damping behavior of 10layer graphene was found to be superior to that of 5layer grapheme, thus raising the prospects that GNPs (20–30 layers) may also exhibit excellent damping properties. Additionally, GNPs have been shown to have intrinsic energy-dissipating mechanisms, such a kinking, bending, sliding and shearing of graphene layers [13]. TaC–GNP composites were prepared with GNP contents of 1 vol.% (TaC-1G), 3 vol.% (TaC-3G) and 5 vol.% (TaC-5G). As-received GNPs (xGNP-M-5, XG Sciences, Lansing, MI, USA) were ultrasonicated in acetone for 90 min in order to alleviate agglomeration. The GNP powder was then mixed with the TaC powder (99.7% purity, 0.36 ± 0.13 lm particle size and 1:1 Ta to C ratio; Inframat Advanced Materials LLC, CT, USA) for 60 min. The powders were consolidated by spark plasma sintering using parameters of 100 MPa and 1850 °C [10,11]. The samples achieved high degrees of densification, with relative densities ranging from 94% to 99%, as shown in Table 1.
1359-6462/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2013.07.030
A. Nieto et al. / Scripta Materialia 69 (2013) 678–681
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Table 1. Summary of TaC–GNP samples used for nanoDMA tests. Sample
GNP content (vol.%)
Relative density (%)
Grain size (lm)
DMA sample thickness (lm)
TaC TaC-1G TaC-3G TaC-5G
None 1 3 5
94.4 ± 0.7 96.9 ± 0.4 97.5 ± 0.4 98.8 ± 0.2
4.5 ± 0.9 3.4 ± 1.6 1.4 ± 0.6 1.4 ± 0.7
190 130 80 150
From the bulk consolidated disks, thin slices were prepared for nanodynamic mechanical analysis (nanoDMA) testing. Samples were mounted in epoxy and then ground to a thickness of 0.5 mm and polished to a 0.1 lm finish. The sample was then retrieved from the mount and the unpolished surface was ground down further and polished to a 0.1 lm finish. The sample was subsequently removed from the mount once again, yielding a thin slice of thickness <200 lm. Such a thin slice was required as the working principle behind nanoDMA mandates that the sample be placed between two rigid bodies – where one rigid body is the indenter tip. If the sample is too thick, then the role of the non-interacting volume may become significant. As shown in Table 1, the thickness of the samples had some variation; however, these differences are not expected to have an impact, given the high hardness and stiffness of TaC. The thin TaC–GNP sample was placed on an Si/SiO2 wafer [12] which has very low damping (tand 0.06) and therefore approximates a rigid body. The nanoDMA experiments were carried out using a TriboIndenter TI 900 (Hysitron Inc., Minneapolis, MN, USA) with a 100 nm Berkovich tip. NanoDMA experiments consist of a quasistatic loading and a low-frequency (<200 Hz) dynamic loading. The nanoDMA tests on TaC–GNP samples were conducted using a 1000 lN quasistatic load with a 7.5% (75 lN) dynamic load. Tests were performed with the dynamic load frequency set at 25, 50, 100 and 200 Hz. Tand is obtained through measurement of the displacement response to the applied force. The angle d is the phase lag between the force applied and the displacement response – a perfectly elastic material would have zero phase lag. A higher lag indicates a higher ratio of viscoelastic to elastic response in the material and thus tand serves as a measure of damping. The values of tand for the different TaC–GNP composites are presented in Figure 1. It can be seen that the GNP improves the damping behavior of the composite in all cases except at a frequency of 200 Hz. The 200 Hz frequency appears to exceed the recovery time needed for the GNP damping mechanisms to be effective. The effect of the GNPs in the TaC-1G sample is negligible – there are not enough GNPs to make an impact. The TaC-3G and TaC-5G show significant improvement in damping behavior. TaC-3G composite shows the highest tand especially at the lower frequencies. The TaC-3G sample shows a damping improvement of 300% over pure TaC at a frequency of 25 Hz. The effect of the GNPs dominates over the potential effects from varying the porosity as the pure TaC sample has the poorest damping despite being the most porous. To begin to understand the effect of GNPs on the damping behavior of TaC–GNP composites, their effect on the overall microstructure should be understood. The
Figure 1. Damping behavior (tand) of TaC–GNP composites at various frequencies.
two principle microstructural features impacted by the GNPs are the grain size and the microstructural homogeneity. Figure 2 presents scanning electron microscopy (SEM) images of the TaC–GNP microstructures as seen from the fracture surfaces. The grain size of the pure TaC sample is the largest, with a slight decrease in the TaC1G sample, while the TaC-3G and TaC-5G samples experienced substantial grain size reduction (Table 1). GNPs have been shown to inhibit grain growth by grain wrapping and grain pinning [14–16]. Additionally, they increase the electrical and thermal conductivity of the composite powder, and thus more uniform heating is achieved during SPS processing. This leads to a higher and more uniform densification of the sample. It should be noted that GNPs become aligned after consolidation, and thus the enhancement in conductivity may display an anisotropic nature. The distribution of GNPs in the sample is dependent on the amount of GNPs used and the powder processing. It can be seen in Figure 2b that the GNP presence in the TaC-1G sample is scarce. The GNPs are mostly found embedded in grains, as seen in the inset of Figure 2b, or as a few isolated agglomerates. The TaC-3G and TaC-5G samples have a significant presence of GNPs. The GNPs are largely oriented perpendicular to the SPS pressing axis [17]. The GNPs in the TaC-3G are widely dispersed and are distributed uniformly throughout the sample, forming a networked structure. The inset of Figure 2c shows GNPs weaving throughout the TaC grains with no signs of agglomeration. The GNPs in the TaC-5G sample are relatively poorly distributed: some areas are saturated with them, while other areas are largely GNP-free (Fig. 2d). The microstructure of the SPS compacts is reflected in the thin slices used for the nanoDMA testing, as can be seen in SEM micrographs of the TaC and TaC3G thin slices in Figure 3. The TaC structure shown in Figure 3a shows a compact and rigid ceramic microstructure that is not conducive to viscoelastic behavior. The mere addition of GNPs is not enough to improve the damping behavior if the amount and dispersion of the GNPs is not adequate. The scarcity of GNPs in
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Figure 2. SEM micrographs of TaC–GNP composites. (a) Pure TaC, (b) TaC-1G, with slight grain size reduction (inset: GNP embedded in TaC grains), (c) TaC-3G, with reduced grain size and homogeneous GNP dispersion (inset: well-dispersed and networked GNPs) and (d) TaC-5G, with significant presence of GNPs and some agglomeration.
the TaC-1G structure leads to the lack of improvement in damping behavior. Likewise, the poor dispersion and uniformity of the GNPs in the TaC-5G sample are the cause of the trend reversal in damping behavior as the GNP content is increased from 3 to 5 vol.%. The TaC3G sample had an adequate amount of GNPs that were effectively disbursed. Figure 3b shows GNPs near the surface of the TaC-3G thin slice where nanoDMA testing was performed. Having established the TaC-3G as the sample with the most effective GNP distribution, the GNP damping mechanisms can now be discussed. Figure 3b shows that GNPs in the TaC matrix display two general kinds of structure: either they are sandwiched between TaC grains or they display a kinked and corrugated structure. Sandwiched GNPs are expected to behave similarly to multi-layer graphene [12]. Weak van der Waals forces will allow the GNPs to exhibit springlike behavior and deform in the out-of-plane direction. The compression of sandwiched GNPs will provide some degree of damping to the TaC matrix. Corrugated GNPs display energy-dissipating mechanisms which are unique to GNPs [13]. Figure 4a shows a kinked GNP in the TaC-3G microstructure. The bending and kinking of GNPs requires energy that would otherwise be used in fracture; hence increasing damping. It can be seen from Figure 4a and b that the GNPs bend at angles greater than 90° without fracturing or tearing. The corrugated GNPs also display platelet sliding. Figure 4b shows two GNPs sliding past one another while maintaining their structural integrity and kinked features. Sliding GNPs enable the transfer of shear forces from TaC grains to the GNPs. The sliding of GNPs in addition to bending provides damping to the TaC matrix. The energy-dissipating mechanisms to improve damping described above can also improve the fracture toughness [10,11]. Table 2 shows the improvement in fracture toughness with varying GNP content. We propose a semi-empirical model here to correlate fracture toughness enhancement with improvement in damping (tand). Improvements in fracture toughness and damping have previously been correlated in plasma-sprayed carbon nanotube-reinforced Al2O3 coatings [18].
Figure 3. SEM micrographs of (a) TaC and (b) TaC-3G thin slices near surfaces where nanoDMA experiments were performed. Rigidly held TaC grains lead to poor damping behavior. GNPs between TaC grains enhance damping behavior in TaC-3G and TaC-5G. Both sandwiched GNPs (yellow solid arrow) and corrugated GNPs (green dotted arrow) are present in the structure, Inset: GNPs are typically present on the surface of the TaC–GNP samples tested. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Figure 4. GNP energy-dissipation mechanisms: (a) GNP sliding, kinking and bending; GNPs are seen to bend at high angles without fracturing; and (b) high-magnification image of GNP kinking while GNPs slide and shear past one another.
The present model factors in the grain size reduction, densification and GNP dispersion. The grain size reduction factor is denoted as K1 and represents the fractional grain size reduction of the TaC–GNP composite as compared to the TaC sample. The reduction in grain size leads to more surfaces that can dissipate energy, thus the factor K1 is positive. The densification factor is denoted as K2 and represents the fractional increase in densification of the TaC–GNP over pure TaC. Increased densification leads to a more rigid structure with less
A. Nieto et al. / Scripta Materialia 69 (2013) 678–681
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Table 2. Summary of enhancement of fracture toughness and damping: the constants used for the model relating toughness to damping (all constants are dimensionless) Tests at 50 Hz frequency were taken as the baseline. Sample
DKIC (%)
D(tand50Hz) (%)
K1
K2
K3
b25Hz
b50Hz
b100Hz
b200Hz
TaC-1G TaC-3G TaC-5G
49 39 99
20 170 140
0.26 0.68 0.69
0.03 0.03 0.05
0.1 0.9 0.3
0 1.53 1.29
1 1 1
0 0.82 0.86
0 0 0.36
porosity; this would decrease damping and hence K2 is negative. The GNP dispersion factor K3 is based solely on qualitative SEM observations of the microstructure. K3 values range from 0 to 1, with 1 being a high level of dispersion and 0 signifying poor dispersion. A high level of dispersion is essential for the effective use of GNPs and thus K3 is positive. The determination of this factor could be further improved upon by using more rigorous methods, such as the dispersion parameter quantification developed by Bakshi et al. [19]. Both toughness (DKIC) and damping enhancement (D(tand)) are relative to the TaC sample and are presented as percentages. The baseline calculations were done for the damping behavior at a frequency of 50 Hz. The variation in the damping behavior due to frequency is taken into account with the factor b. The model proposed is presented in Eq. (1): Dðtan dÞ ¼ bðaK 1 bK 2 þ cK 3 ÞDðK IC Þ
ð1Þ
The constants a, b and c are calculated by fitting the experimental results (these constants are dimensionless). Eq. (2) presents the model with the fitted values; the model correlates the fracture toughness enhancement with the damping enhancement within the experimental margins of error: 1 Dðtan dÞ ¼ b K 1 7K 2 þ 5K 3 DðK IC Þ ð2Þ 2 The factors and parameters used in the model above are presented in Table 2. The b values are relative to the corresponding value at a frequency of 50 Hz. A value above 1 indicates that the enhancement of damping was greater than in the 50 Hz test; likewise, a value of less than 1 indicates that the damping was less. A value of zero indicates no improvement in damping over the TaC samples and a negative value indicates that the damping behavior decreased relative to the TaC sample. As previously discussed, damping enhancement dies down at 200 Hz and is generally higher at lower frequencies. The role of GNP dispersion is elucidated in the model; wide dispersion is critical to effective damping enhancement. The TaC-3G sample displays such wide dispersion, and this corresponds to the highest improvement in damping. The highest enhancement in fracture toughness is obtained by the TaC-5G, indicating that the toughness is more sensitive to the amount of GNPs than the dispersion. This study demonstrates that the intrinsic energy-dissipating mechanisms of GNPs can
be utilized in a composite material to enhance the fracture toughness and damping behavior of the UHTC TaC. The authors acknowledge Dr. Ali Sayir, Program Manager of High Temperature Aerospace Materials at the Air Force Office of Scientific Research, and the receipt of Grants FA9550-11-1-0334 and FA9550-12-10263. The authors also acknowledge the support from the Advanced Materials Engineering Research Institute (AMERI). [1] T.H. Squire, J. Marschall, J. Eur. Ceram. Soc. 30 (2010) 2239–2251. [2] P.L. Moses, V.L. Rausch, L.T. Nguyen, J.R. Hill, Acta Astronaut. 55 (2004) 619–630. [3] J.W. Canan, Aerosp. Am. 11 (2007) 26–31. [4] S. Guicciardi, L. Silvestroni, M. Nygren, D. Sciti, J. Am. Ceram. Soc. 93 (2010) 2384–2391. [5] L. Silvestroni, D. Sciti, S. Guicciardi, C. Melandri, J. Eur. Ceram. 30 (2010) 2155–2164. [6] J. Zou, G.-J. Zhang, C.-F. Hu, T. Nishimura, Y. Sakka, H. Tanaka, J. Vleugels, O. Van der Biest, J. Eur. Ceram. Soc. 32 (2012) 2527–2529. [7] S.R. Bakshi, V. Musaramthota, D.A. Virzi, A.K. Keshri, D. Lahiri, V. Singh, S. Seal, A. Agarwal, Mater. Sci. Eng., A 528 (2011) 2538–2547. [8] D. Lahiri, E. Khaleghi, S.R. Bakshi, W. Li, E. Olevsky, A. Agarwal, Scripta Mater. 68 (2013) 285–288. [9] F. Yang, X. Zhang, J. Han, S. Du, J. Alloy. Compd. 472 (2009) 395–399. [10] A. Nieto, Thesis and Dissertations, Florida International University, March 2013. [11] A. Nieto, D. Lahiri, A. Agarwal, Mater. Sci. Eng., A 582 (2013) 338–346. [12] D. Lahiri, S. Das, W. Choi, A. Agarwal, ACS Nano 6 (2012) 3992–4000. [13] A. Nieto, D. Lahiri, A. Agarwal, Carbon 50 (2012) 4068– 4077. [14] K. Wang, Y. Wang, Z. Fan, J. Yan, T. Wei, Mater. Res. Bull. 46 (2011) 315–318. [15] L.S. Walker, V.R. Marotto, M.A. Rafiee, N. Koratkar, E.L. Corral, ACS Nano 5 (2011) 3182–3190. [16] J. Dusza, J. Morgiel, A. Duszova, L. Kvetkova, M. Nosko, P. Kun, C. Balazsi, J. Eur. Ceram. Soc. 32 (2012) 3389–3397. [17] C. Ramirez, F.M. Figueiredo, P. Miranzo, P. Poza, M.I. Osendi, Carbon 50 (2012) 3607–3615. [18] K. Balani, A. Agarwal, J. Appl. Phys. 104 (2008) 063517. [19] S.R. Bakshi, R.G. Batista, A. Agarwal, Compos. A 40 (2009) 1311–1318.
ScienceDirect Scripta Materialia 69 (2013) 678–681 www.elsevier.com/locate/scriptamat
Nanodynamic mechanical behavior of graphene nanoplatelet-reinforced tantalum carbide Andy Nieto,a Debrupa Lahiria,b and Arvind Agarwala,⇑ a
Plasma Forming Laboratory, Nanomechanics and Nanotribology Laboratory, Mechanical and Materials Engineering, Florida International University, 10555 West Flagler Street, EC 3464, Miami, FL 33174, USA b Department of Materials and Metallurgical Engineering, Indian Institute of Technology, Roorkee, Uttarakhand 247667, India Received 6 June 2013; revised 26 July 2013; accepted 27 July 2013 Available online 1 August 2013
Nanodynamic mechanical analysis (nanoDMA) is performed on spark plasma sintered tantalum carbide composites reinforced with graphene nanoplatelets (GNPs). The addition of GNPs enhances damping (tand) at 25–100 Hz frequencies by up to 300%. It also improves damping behavior through energy-dissipating mechanisms, such as GNP bending, kinking and sliding. A model for correlating improvement in the damping behavior with the fracture toughness is presented. GNP energy-dissipating mechanisms are most effective in improving damping behavior when GNPs are dispersed uniformly. Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: TaC; NanoDMA; Graphene nanoplatelet; Damping; Tan delta
Ultrahigh-temperature ceramics (UHTCs) have attracted much attention because of their excellent refractory properties and high strength. These properties make them ideal candidates for aerospace systems, such as hypersonic missiles, planetary entry vehicles and rocket propulsion systems [1–3]. One of the factors impeding the implementation of these materials is their low fracture toughness. Several studies have been conducted on composite UHTCs designed to improve fracture toughness and flexure strength [4–9]. One crucial property of UHTCs that has received little attention is their poor damping behavior. UHTCs such as tantalum carbide (TaC) will be utilized in hypersonic systems that are subjected to a barrage of shock waves. Shock waves are unsteady phenomena which impart impulse forces onto the surface generating them. Damping of such impulsive forces is critical to preventing accumulative damage. Hypersonic vehicles and spacecraft are also subjected to substantial amounts of vibrations and flutter, which can cause cracking. Improving the dissipation of vibrations can suppress crack nucleation and thus reduce the amount of critical cracks and defects. Our approach utilizes the addition of graphene nanoplatelets (GNPs) as reinforcement for TaC to enhance both the fracture toughness and the damping behavior.
⇑ Corresponding
author. Tel.: +1 305 348 1701; fax: +1 305 348 1932; e-mail: agarwala@fiu.edu
The details of TaC–GNP composite synthesis, microstructure and fracture toughness can be found elsewhere [10,11]. The motive behind using GNPs as a dampening phase stems from the excellent damping behavior of multi-layer graphene [12]. Lahiri et al. [12] showed that multi-layer graphene membranes improved the damping behavior of a rigid Si/SiO2 surface by up to 260%. The improvement in damping behavior (tan d) was seen at various dynamic loads (0.1–50 lN) and for a range of frequencies (50–250 Hz). The damping behavior of 10layer graphene was found to be superior to that of 5layer grapheme, thus raising the prospects that GNPs (20–30 layers) may also exhibit excellent damping properties. Additionally, GNPs have been shown to have intrinsic energy-dissipating mechanisms, such a kinking, bending, sliding and shearing of graphene layers [13]. TaC–GNP composites were prepared with GNP contents of 1 vol.% (TaC-1G), 3 vol.% (TaC-3G) and 5 vol.% (TaC-5G). As-received GNPs (xGNP-M-5, XG Sciences, Lansing, MI, USA) were ultrasonicated in acetone for 90 min in order to alleviate agglomeration. The GNP powder was then mixed with the TaC powder (99.7% purity, 0.36 ± 0.13 lm particle size and 1:1 Ta to C ratio; Inframat Advanced Materials LLC, CT, USA) for 60 min. The powders were consolidated by spark plasma sintering using parameters of 100 MPa and 1850 °C [10,11]. The samples achieved high degrees of densification, with relative densities ranging from 94% to 99%, as shown in Table 1.
1359-6462/$ - see front matter Ó 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.scriptamat.2013.07.030
A. Nieto et al. / Scripta Materialia 69 (2013) 678–681
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Table 1. Summary of TaC–GNP samples used for nanoDMA tests. Sample
GNP content (vol.%)
Relative density (%)
Grain size (lm)
DMA sample thickness (lm)
TaC TaC-1G TaC-3G TaC-5G
None 1 3 5
94.4 ± 0.7 96.9 ± 0.4 97.5 ± 0.4 98.8 ± 0.2
4.5 ± 0.9 3.4 ± 1.6 1.4 ± 0.6 1.4 ± 0.7
190 130 80 150
From the bulk consolidated disks, thin slices were prepared for nanodynamic mechanical analysis (nanoDMA) testing. Samples were mounted in epoxy and then ground to a thickness of 0.5 mm and polished to a 0.1 lm finish. The sample was then retrieved from the mount and the unpolished surface was ground down further and polished to a 0.1 lm finish. The sample was subsequently removed from the mount once again, yielding a thin slice of thickness <200 lm. Such a thin slice was required as the working principle behind nanoDMA mandates that the sample be placed between two rigid bodies – where one rigid body is the indenter tip. If the sample is too thick, then the role of the non-interacting volume may become significant. As shown in Table 1, the thickness of the samples had some variation; however, these differences are not expected to have an impact, given the high hardness and stiffness of TaC. The thin TaC–GNP sample was placed on an Si/SiO2 wafer [12] which has very low damping (tand 0.06) and therefore approximates a rigid body. The nanoDMA experiments were carried out using a TriboIndenter TI 900 (Hysitron Inc., Minneapolis, MN, USA) with a 100 nm Berkovich tip. NanoDMA experiments consist of a quasistatic loading and a low-frequency (<200 Hz) dynamic loading. The nanoDMA tests on TaC–GNP samples were conducted using a 1000 lN quasistatic load with a 7.5% (75 lN) dynamic load. Tests were performed with the dynamic load frequency set at 25, 50, 100 and 200 Hz. Tand is obtained through measurement of the displacement response to the applied force. The angle d is the phase lag between the force applied and the displacement response – a perfectly elastic material would have zero phase lag. A higher lag indicates a higher ratio of viscoelastic to elastic response in the material and thus tand serves as a measure of damping. The values of tand for the different TaC–GNP composites are presented in Figure 1. It can be seen that the GNP improves the damping behavior of the composite in all cases except at a frequency of 200 Hz. The 200 Hz frequency appears to exceed the recovery time needed for the GNP damping mechanisms to be effective. The effect of the GNPs in the TaC-1G sample is negligible – there are not enough GNPs to make an impact. The TaC-3G and TaC-5G show significant improvement in damping behavior. TaC-3G composite shows the highest tand especially at the lower frequencies. The TaC-3G sample shows a damping improvement of 300% over pure TaC at a frequency of 25 Hz. The effect of the GNPs dominates over the potential effects from varying the porosity as the pure TaC sample has the poorest damping despite being the most porous. To begin to understand the effect of GNPs on the damping behavior of TaC–GNP composites, their effect on the overall microstructure should be understood. The
Figure 1. Damping behavior (tand) of TaC–GNP composites at various frequencies.
two principle microstructural features impacted by the GNPs are the grain size and the microstructural homogeneity. Figure 2 presents scanning electron microscopy (SEM) images of the TaC–GNP microstructures as seen from the fracture surfaces. The grain size of the pure TaC sample is the largest, with a slight decrease in the TaC1G sample, while the TaC-3G and TaC-5G samples experienced substantial grain size reduction (Table 1). GNPs have been shown to inhibit grain growth by grain wrapping and grain pinning [14–16]. Additionally, they increase the electrical and thermal conductivity of the composite powder, and thus more uniform heating is achieved during SPS processing. This leads to a higher and more uniform densification of the sample. It should be noted that GNPs become aligned after consolidation, and thus the enhancement in conductivity may display an anisotropic nature. The distribution of GNPs in the sample is dependent on the amount of GNPs used and the powder processing. It can be seen in Figure 2b that the GNP presence in the TaC-1G sample is scarce. The GNPs are mostly found embedded in grains, as seen in the inset of Figure 2b, or as a few isolated agglomerates. The TaC-3G and TaC-5G samples have a significant presence of GNPs. The GNPs are largely oriented perpendicular to the SPS pressing axis [17]. The GNPs in the TaC-3G are widely dispersed and are distributed uniformly throughout the sample, forming a networked structure. The inset of Figure 2c shows GNPs weaving throughout the TaC grains with no signs of agglomeration. The GNPs in the TaC-5G sample are relatively poorly distributed: some areas are saturated with them, while other areas are largely GNP-free (Fig. 2d). The microstructure of the SPS compacts is reflected in the thin slices used for the nanoDMA testing, as can be seen in SEM micrographs of the TaC and TaC3G thin slices in Figure 3. The TaC structure shown in Figure 3a shows a compact and rigid ceramic microstructure that is not conducive to viscoelastic behavior. The mere addition of GNPs is not enough to improve the damping behavior if the amount and dispersion of the GNPs is not adequate. The scarcity of GNPs in
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A. Nieto et al. / Scripta Materialia 69 (2013) 678–681
Figure 2. SEM micrographs of TaC–GNP composites. (a) Pure TaC, (b) TaC-1G, with slight grain size reduction (inset: GNP embedded in TaC grains), (c) TaC-3G, with reduced grain size and homogeneous GNP dispersion (inset: well-dispersed and networked GNPs) and (d) TaC-5G, with significant presence of GNPs and some agglomeration.
the TaC-1G structure leads to the lack of improvement in damping behavior. Likewise, the poor dispersion and uniformity of the GNPs in the TaC-5G sample are the cause of the trend reversal in damping behavior as the GNP content is increased from 3 to 5 vol.%. The TaC3G sample had an adequate amount of GNPs that were effectively disbursed. Figure 3b shows GNPs near the surface of the TaC-3G thin slice where nanoDMA testing was performed. Having established the TaC-3G as the sample with the most effective GNP distribution, the GNP damping mechanisms can now be discussed. Figure 3b shows that GNPs in the TaC matrix display two general kinds of structure: either they are sandwiched between TaC grains or they display a kinked and corrugated structure. Sandwiched GNPs are expected to behave similarly to multi-layer graphene [12]. Weak van der Waals forces will allow the GNPs to exhibit springlike behavior and deform in the out-of-plane direction. The compression of sandwiched GNPs will provide some degree of damping to the TaC matrix. Corrugated GNPs display energy-dissipating mechanisms which are unique to GNPs [13]. Figure 4a shows a kinked GNP in the TaC-3G microstructure. The bending and kinking of GNPs requires energy that would otherwise be used in fracture; hence increasing damping. It can be seen from Figure 4a and b that the GNPs bend at angles greater than 90° without fracturing or tearing. The corrugated GNPs also display platelet sliding. Figure 4b shows two GNPs sliding past one another while maintaining their structural integrity and kinked features. Sliding GNPs enable the transfer of shear forces from TaC grains to the GNPs. The sliding of GNPs in addition to bending provides damping to the TaC matrix. The energy-dissipating mechanisms to improve damping described above can also improve the fracture toughness [10,11]. Table 2 shows the improvement in fracture toughness with varying GNP content. We propose a semi-empirical model here to correlate fracture toughness enhancement with improvement in damping (tand). Improvements in fracture toughness and damping have previously been correlated in plasma-sprayed carbon nanotube-reinforced Al2O3 coatings [18].
Figure 3. SEM micrographs of (a) TaC and (b) TaC-3G thin slices near surfaces where nanoDMA experiments were performed. Rigidly held TaC grains lead to poor damping behavior. GNPs between TaC grains enhance damping behavior in TaC-3G and TaC-5G. Both sandwiched GNPs (yellow solid arrow) and corrugated GNPs (green dotted arrow) are present in the structure, Inset: GNPs are typically present on the surface of the TaC–GNP samples tested. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Figure 4. GNP energy-dissipation mechanisms: (a) GNP sliding, kinking and bending; GNPs are seen to bend at high angles without fracturing; and (b) high-magnification image of GNP kinking while GNPs slide and shear past one another.
The present model factors in the grain size reduction, densification and GNP dispersion. The grain size reduction factor is denoted as K1 and represents the fractional grain size reduction of the TaC–GNP composite as compared to the TaC sample. The reduction in grain size leads to more surfaces that can dissipate energy, thus the factor K1 is positive. The densification factor is denoted as K2 and represents the fractional increase in densification of the TaC–GNP over pure TaC. Increased densification leads to a more rigid structure with less
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Table 2. Summary of enhancement of fracture toughness and damping: the constants used for the model relating toughness to damping (all constants are dimensionless) Tests at 50 Hz frequency were taken as the baseline. Sample
DKIC (%)
D(tand50Hz) (%)
K1
K2
K3
b25Hz
b50Hz
b100Hz
b200Hz
TaC-1G TaC-3G TaC-5G
49 39 99
20 170 140
0.26 0.68 0.69
0.03 0.03 0.05
0.1 0.9 0.3
0 1.53 1.29
1 1 1
0 0.82 0.86
0 0 0.36
porosity; this would decrease damping and hence K2 is negative. The GNP dispersion factor K3 is based solely on qualitative SEM observations of the microstructure. K3 values range from 0 to 1, with 1 being a high level of dispersion and 0 signifying poor dispersion. A high level of dispersion is essential for the effective use of GNPs and thus K3 is positive. The determination of this factor could be further improved upon by using more rigorous methods, such as the dispersion parameter quantification developed by Bakshi et al. [19]. Both toughness (DKIC) and damping enhancement (D(tand)) are relative to the TaC sample and are presented as percentages. The baseline calculations were done for the damping behavior at a frequency of 50 Hz. The variation in the damping behavior due to frequency is taken into account with the factor b. The model proposed is presented in Eq. (1): Dðtan dÞ ¼ bðaK 1 bK 2 þ cK 3 ÞDðK IC Þ
ð1Þ
The constants a, b and c are calculated by fitting the experimental results (these constants are dimensionless). Eq. (2) presents the model with the fitted values; the model correlates the fracture toughness enhancement with the damping enhancement within the experimental margins of error: 1 Dðtan dÞ ¼ b K 1 7K 2 þ 5K 3 DðK IC Þ ð2Þ 2 The factors and parameters used in the model above are presented in Table 2. The b values are relative to the corresponding value at a frequency of 50 Hz. A value above 1 indicates that the enhancement of damping was greater than in the 50 Hz test; likewise, a value of less than 1 indicates that the damping was less. A value of zero indicates no improvement in damping over the TaC samples and a negative value indicates that the damping behavior decreased relative to the TaC sample. As previously discussed, damping enhancement dies down at 200 Hz and is generally higher at lower frequencies. The role of GNP dispersion is elucidated in the model; wide dispersion is critical to effective damping enhancement. The TaC-3G sample displays such wide dispersion, and this corresponds to the highest improvement in damping. The highest enhancement in fracture toughness is obtained by the TaC-5G, indicating that the toughness is more sensitive to the amount of GNPs than the dispersion. This study demonstrates that the intrinsic energy-dissipating mechanisms of GNPs can
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